The announcement came as divers pulled body parts, wreckage and clothing from waters off Jakarta.

"We have located the position of the black boxes, both of them," said Soerjanto Tjahjanto, head of National Transportation Safety Commission (KNKT).

"Divers will start looking for them now and hopefully it won't be long before we get them."

The Sriwijaya Air Boeing 737-500 went into a steep dive about four minutes after it left Soekarno-Hatta international airport in Jakarta on Saturday afternoon.

President Joko "Jokowi" Widodo expressed his "deep condolences", and called on citizens to "pray together so that victims can be found".

But the frantic search involving helicopters and a flotilla of warships appeared to offer no hope of finding any survivors.

The search and rescue agency said it had so far collected five body bags with human remains as well as debris from the crash site in the Java Sea.

A piece of child's clothing, a broken tyre and wheel, life jackets and wreckage from the plane's body were found, according to authorities and AFP reporters on the scene.

Among the passengers was Beben Sofian, 59, and her husband Dan Razanah, 58.

"They took a selfie and sent it to their kids before taking off," the couple's nephew Hendra told AFP.

All 62 people on board, passengers and crew, were Indonesian, authorities said. The count included 10 children.

Distraught relatives waited nervously for news at the airport in Pontianak, the city on Indonesia's section of Borneo island which had been flight SJ182's destination, about 90 minutes flying time over the Java Sea.

"I have four family members on the flight -- my wife and three children," Yaman Zai said on Saturday evening as he sobbed.

"(My wife) sent me a picture of the baby today... How could my heart not be torn into pieces?"